A new battery technology called STAIR (St Andrews Air) promises to be lighter than your typical lithium ion battery while holding 5-10x the power.

The battery charges and recharges like normal, but during discharge, atmospheric oxygen penetrates the battery and reacts with internal carbon as a reagent. This reaction creates more energy, and they best part about it is that you didn't need to carry around the extra weight of the oxygen in your backpack. (Of course, sacrificing our air might not be the best way to build a next generation battery.)